The Senate is poised to begin the most wide-ranging and ambitious battle over gun control on Capitol Hill in 20 years, with a vote scheduled Thursday that would formally start the debate.

News of that vote was a boost for the Obama administration, which has lobbied hard for increased background checks on potential gun buyers and for new limits on assault rifles and high-capacity ammunition magazines. All will face heavy opposition from the National Rifle Association and its Capitol Hill allies in both parties.

Democratic Sen. Joe Manchin III (W.Va.) and Republican Sen. Patrick J. Toomey (Pa.), who have been supported in the past by the NRA and have been negotiating a bill on expanded background checks, are planning a news conference Wednesday morning at which the details of a deal could be announced, people familiar with the negotiations said.

The developments came on a day in which the subject of gun control — and emotional reminders of gun violence — overtook Washington. On Capitol Hill, relatives of those killed in December’s mass shooting in Newtown, Conn., made solemn visits to senators’ offices. On the Senate floor, Majority Leader Harry M. Reid (D-Nev.) mentioned his father’s death by self-inflicted gunshot.

The Democratic-led Senate is expected to reject President Obama’s proposals to ban military-style assault rifles and to limit the size of high-capacity magazines. And even Obama’s proposals for expanded background checks could be watered down. The NRA is working on alternatives that could be introduced during a Senate debate.

In an ominous sign for the president, at least two Democratic senators — Mark Pryor (Ark.) and Max Baucus (Mont.) — said Tuesday that they are unsure whether they can support him.

On Thursday, the Senate is scheduled to vote on a “motion to proceed” — essentially giving itself permission to consider a gun-control bill.

Sixty votes are needed to overcome a filibuster threatened by some conservative Republicans, and the votes appear to be there.

“I am not going to join in a filibuster against bringing the bill to the floor as long as there is ample opportunity for amendments,” said Sen. Susan Collins (R-Maine). She was one of at least eight Republicans who seemed likely to join with most of the 55 Democrats in voting to proceed.

On Tuesday — even before it formally began — the gun debate appeared to be something different on Capitol Hill. That was evident in the halls of the Senate office buildings, where a small group of people moved silently among the talkative crowds of tourists, staff members and glad-handers with name tags.

They were relatives of those killed at Sandy Hook Elementary School in Newtown, 11 people representing eight families. They wouldn’t say whom they were planning to meet with.

It was an attempt to influence politics, without giving up the power or privacy of their grief.

“We’re not political. We’re just moms and dads and husbands and wives,” said Bill Sherlach, whose wife, Mary Sherlach, a psychologist at Sandy Hook, was killed along with five other women and 20 children on Dec. 14. “We see the obvious, and we’re not caught up in the political trappings.”

But this was Congress. Their effort to avoid politics lasted all the way to the door of the first office they visited. There, Sen. Richard Blumenthal (D-Conn.) greeted them with hugs in front of the assembled news cameras.

Later in the day, the same solemn group visited the office of Sen. Johnny Isakson (R-Ga.). They closed the door behind them. Isakson then opened it. “Why don’t y’all come on out?” he said. “We’re not going far.”

The senator led the group back out into the hallway, to walk the 13 paces from Room SR-131 to Room SR-132. As TV cameras filmed, he opened the door and held it while the group filed in.

Isakson, who has expressed openness in the past to increased background checks, is part of a small bipartisan group of senators that could control the fate and the content of a potential gun bill. The group also includes Manchin and Toomey.

Manchin and Toomey have discussed expanding background checks to all commercial sales — whether at gun shows, via the Internet or in any circumstance that involved paid advertising, according to people familiar with their conversations. That would be more stringent than the current rule, which requires checks only when purchases are made through a licensed dealer.

But background checks would not be required for many sales between private individuals.

That would stop short of a proposal offered by Sen. Charles E. Schumer (D-N.Y.) and backed by the White House that would require background checks for nearly every kind of sale.

Toomey has been under pressure to make progress on firearms-related issues. Pennsylvania’s other senator, Robert P. Casey Jr. (D), broke with the NRA after the Newtown shootings, and political organizing around gun control has increased lately in Pennsylvania, in part the result of funding from Mayors Against Illegal Guns, an organization funded by New York Mayor Michael R. Bloomberg (I).

But there is also strong pressure from the other side. In Toomey’s office on Tuesday, a receptionist assured one unhappy caller that the senator is a strong supporter of the Second Amendment.

There was a pause on her end. The caller was asking about the one area in which Toomey’s position is unclear.

“The senator himself has not released a statement on background checks yet,” she said.

The next step is the vote planned for Thursday. It’s necessary because of a filibuster threat led by the Senate’s conservative wing, which wants to block the Senate from debating a gun-control bill.

For now, it looks as though that effort will fail.

Some Republicans said they would vote with Democrats to end any filibuster and let the debate begin. Democrats need their votes because they cannot count on the votes of all 55 of their senators.

If Reid can get 60 votes, the debate will begin. And then things will get complicated.

Senators from both parties are likely to introduce numerous amendments. One might establish an online portal for background checks and provide more federal funding for mental health programs assisting veterans of the wars in Iraq and Afghanistan. There also probably will be amendments backed by the NRA, designed to make the bill less onerous for gun owners and buyers.

Any bill would need only a majority of votes to pass. After that, it would go to the GOP-led House, where another long process could begin.